What are Bevel Edges
The bevel weight is visualized in light blue (similiar to the teal sharp).

You can edit the weight in Edit Mode by selecting edges and pressing &#9096; CtrlE to open up the edge menu (which can also be accessed through the 3d View's header menu bar). 
In the edge menu choose Edit Bevel Weight. The bevel weight can also be accessed in the Properties Panel N of the 3D View. The bevel modifier can use the bevel weight to restrict the beveling.